The custom of burying the Alleluias during Lenten worship appears to go back for many centuries, perhaps as early as the fifth century.
I browsed around and found the following at the Canberra Traditional Latin Mass Community:
The depositio (discontinuance) of the Alleluia on the eve of Septuagesima assumed in mediæval times a solemn and emotional note of saying farewell to the beloved song. Despite the fact that Pope Alexander II [in the eleventh century] had ordered a very simple and sombre way of "deposing" the Alleluia, a variety of farewell customs prevailed in many countries up to the sixteenth century...
In some French churches the custom developed in ancient times of allowing the congregation to take part in the celebration of a quasi-liturgical farewell ceremony. The clergy abstained from any role in this popular service. Choirboys officiated in their stead at what was called "Burial of the Alleluia" performed the Saturday afternoon before Septuagesima Sunday. We find a description of it in the fifteenth-century statute book of the church of Toul:
"On Saturday before Septuagesima Sunday all choir boys gather in the sacristy during the prayer of the None, to prepare for the burial of the Alleluia. After the last Benedicámus (i.e., at the end of the service) they march in procession with crosses, tapers, holy water and censers; and they carry a coffin, as in a funeral. Thus they proceed through the aisle, moaning and morning, until they reach the cloister. There they bury the coffin; they sprinkle it with holy water and incense it; whereupon they return to the sacristy by the same way."
In Paris, a straw figure bearing in golden letters the inscription "Alleluia" was carried out of the choir at the end of the service, and burned in the churchyard [...]
Thus the Alleluia is sung for the last time, and not heard again until it suddenly bursts into glory during the Mass of the Easter Vigil, when the celebrant intones this sacred word after the Epistle, repeating it three times as a jubilant herald of the Resurrection of Christ.
Father Franz Xaver WEISER SJ
Handbook of Christian Feasts and Customs (Harcourt, 1958)
The Anglican Curmudgeon posted this video a year ago before Lent 2009. Some of us could not help but watch it during Lent. I saw, but did not hear, any alleluias. Did I break my discipline? Will you be breaking yours today if you watch the video?